Magnetic island merger as a mechanism for inverse magnetic energy transfer

Muni Zhou,Pallavi Bhat,Dmitri A. Uzdensky,Nuno F. Loureiro

doi:10.1103/physrevresearch.1.012004

Abstract

Magnetic energy transfer from small to large scales due to successive magnetic island coalescence is investigated. A solvable analytical model is introduced and shown to correctly capture the evolution of the main quantities of interest, as borne out by numerical simulations. Magnetic reconnection is identified as the key mechanism enabling the inverse transfer, and setting its properties: magnetic energy decays as $\tilde t^{-1}$, where $\tilde t$ is time normalized to the (appropriately defined) reconnection timescale; and the correlation length of the field grows as $\tilde t^{1/2}$. The magnetic energy spectrum is self-similar, and evolves as $\propto \tilde t ^{-3/2}k^{-2}$, where the $k$-dependence is imparted by the formation of thin current sheets.

Highlights

Rapid CommunicationsMagnetic island merger as a mechanism for inverse magnetic energy transfer Muni Zhou, Pallavi Bhat, Nuno F
The transfer of magnetic energy from small to large spatial scales is a poorly understood plasma process of fundamental relevance to a variety of space and astrophysical environments
Past theoretical work on inverse magnetic energy transfer has mainly developed along two directions: (i) the study of magnetohydrodynamic (MHD) turbulence (e.g., Refs. [9,10,11,12,13,14,15,16,17,18]), where the inverse transfer arises from the conservation of the square vector potential in two-dimensional (2D) systems [19,20] and magnetic helicity in threedimensional (3D) systems [21,22], and (ii) the long-term evolution of Weibel-generated current filaments via their coalescence [3,23,24,25,26,27]

Summary

Rapid Communications

Magnetic island merger as a mechanism for inverse magnetic energy transfer Muni Zhou, Pallavi Bhat, Nuno F. Uzdensky3 1Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. Magnetic energy transfer from small to large scales due to successive magnetic island coalescence is investigated. A solvable analytical model is introduced and shown to correctly capture the evolution of the main quantities of interest, as borne out by direct numerical simulations. Magnetic reconnection is identified as the key mechanism enabling the inverse transfer, and setting its properties: Magnetic energy decays as t−1, where tis time normalized to the (appropriately defined) reconnection timescale, and the correlation length of the field grows as t1/2. The magnetic energy spectrum is self-similar, and evolves as ∝t−3/2k−2, where the k dependence is imparted by the formation of thin current sheets

Introduction

Published by the American Physical Society

Conclusions